# A question of notation

1. Jul 14, 2010

### Zorba

In a book I am reading I see the following:

$$m(B_n) \uparrow m(A)\quad \textrm{if}\, B_1 \subset B_2 \subset \dots\, \textrm{and}\, \bigcup_{n=1}^{\infty} B_n = A$$

What does the up arrow signify? m(A) denotes the lebesgue measure of A if that helps.

2. Jul 15, 2010

### Staff: Mentor

My guess is that it means "approaches from below." IOW m(Bn) < m(A) for all n, but as n increases the difference between m(Bn) and m(A) becomes smaller.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook